a) Field of the Invention
The present invention relates to a method for measuring distributed dispersion of gradient-index optical elements and an optical system to be used for carrying out the method.
b) Description of the Prior Art:
In the recent years, gradient-index optical elements have been used increasingly as pickups for video disks and copying machines. Further, relatively small gradient-index optical elements such as optical wave guides and planar microlenses are being put to practical use in a field of opto-electronics, whereas gradient-index optical elements having relatively large diameters are being adopted in lens systems for cameras using silver salt diffusion transfer process, video cameras and microscopes and so on in a field of image processing.
Since these gradient-index optical elements have characteristics which are largely variable dependently on refractive index profiles thereof, it is necessary for practical use of these gradient-index optical elements to measure data on the refractive index profiles of the gradient-index optical elements with high accuracy.
When a gradient-index optical element is to be adopted in the field of opto-electronics wherein the optical element is to be used mainly at a single wavelength, it is sufficient to measure a refractive index profile only at the intended wavelength. When a gradient-index optical element is to be adopted in the field of image processing wherein the optical element is to be used mainly within a broad wavelength region, in contrast, it is necessary to accurately measure a refractive index profile and distributed dispersion at a main wavelength (a wavelength selected as a standard).
Under the present circumstance, there has been proposed no method yet for measuring accurately and directly distributed dispersion of a gradient-index optical element, but it is known to those skilled in the art that distributed dispersion can be determined from refractive index profiles measured at a plurality of wavelengths. Accordingly, methods for measuring refractive index profiles will be described below as the prior art.
As the conventional methods for measuring refractive index profiles, there are known the longitudinal interference method which permits determining refractive index profiles by observing, through an interference microscope, thin samples sliced and polished in a direction perpendicular to center axes of the refractive index profiles, and by calculating optical path differences per unit thickness of the thin samples, as well as the traverse interference method which permits determining refractive index profiles by tracing rays while allowing the rays in directions perpendicular to the center axes of the refractive index profiles of cylindrical samples to be measured.
More recently, Japanese Patent Preliminary Publication No. Sho 63-275936 has proposed another method for measuring refractive index profiles. The principle of Pulfrich refractometer, which is well known to those skilled in the art, is applied to this method. A system for carrying out this method is illustrated in FIG. 1, wherein a sample 101 which is to be subjected to the measurement of a refractive index profile is mounted on a hemispherical sample stage 102 so that a measuring surface of the sample 101 is in close contract with a sample mounting surface 102A of the sample stage 102, and a laser beam 105 is focused by a condenser lens 103 onto a measuring point 104 on the mounting surface 102A through a hemispherical surface 102B other than the sample mounting surface 102A. Since light beams which are allowed to be incident on the measuring point 104 within a range of angles of incidence larger than a critical angle of total reflection .phi..sub.c are totally reflected, reflected light beams having brightness nearly equal to the incident light beams are obtained within a region of 106, whereas most of light beams which are allowed to be incident on the measuring point 104 within another range of angles of incidence smaller than the critical angle .phi..sub.c transmit outside through the measuring point 104 and reflected light beams having brightness lower than that of the incident light beams are obtained within another region 107. By measuring a light bundle which is reflected by the measuring point 104, it is therefore possible to measure a section 109 of the light bundle on which the relatively bright region 106 and the relatively dark region 107 are formed on both sides of a bright-dark boundary 108. Since a ray which is allowed to be incident on the measuring point 104 at the critical angle .phi..sub.c of total reflection is reflected to the boundary 108 located between the bright region and the dark region, it is possible to determine the critical angle of total reflection by measuring an angle of the boundary between the bright and dark regions relative to a normal to the measuring surface, and calculate a refractive index n of the sample 101 at the measuring point 104 from a known refractive index of the sample stage by using the following formula (1): EQU n=n.sub.o sin .phi..sub.c ( 1).
Furthermore, it is possible to measure a refractive index profile of the sample 101 by displacing the sample 101 in the horizontal direction while it is kept in close contact with the sample stage 102.
Since dispersion at each point of the sample 101 is calculated from refractive indices which are measured in absolute at a plurality of wavelengths, determination of distributed dispersion by utilizing the conventional methods for measuring refractive index profiles poses problems that refractive indices of one and the same position of a sample at a plurality of wavelengths must be selected accurately, after measurements and that errors involved in data obtained by measurements inevitably produce large influence on determination of the distributed dispersion. As a result, it is obliged to adopt, for determining distributed dispersion with high accuracy, complicated and expensive members for obtaining position data.
Moreover, the longitudinal and traverse interference methods measure refractive index differences, i.e., relative refractive index profiles with high accuracies, but do not allow to determine dispersion directly from the data obtained by the measurements at the plurality of wavelengths. These method do not permit determining distributed dispersion without using refractive indices measured in absolute values by another method at the same positions and at the plurality of wavelength in combination with the refractive index profiles measured by the longitudinal or traverse interference method.
In addition, the method proposed by Japanese Patent Preliminary Publication No. Sho 63-275936 is intended to be applied only to the field of opto-electronics, adapted to measure a refractive index profile at a single wavelength and therefore insufficient for accurate determination of distributed dispersion by the measurements of refractive index profiles at a plurality of wavelengths.